Question

for a moving object, the force acting on the object varies directly with the objects acceleration. when a force of 90 n acts on a certain object, the acceleration of the object is 10 m/s². if the acceleration of the object becomes 6 m/s², what is the force?

Explanation:

Step1: Find the constant of proportionality

Since \(F = k\times a\) (where \(F\) is force, \(a\) is acceleration and \(k\) is the constant of proportionality). Given \(F = 90\) N and \(a=10\) m/s². Substitute into the formula: \(90=k\times10\), then \(k=\frac{90}{10}=9\).

Step2: Calculate the new force

Now \(a = 6\) m/s² and \(k = 9\). Using \(F=k\times a\), we substitute \(k = 9\) and \(a = 6\) into the formula: \(F=9\times6 = 54\).

Answer:

\(54\)